Consistent deformations of [p,p]-type gauge field theories

TL;DR

This paper uses BRST cohomology to analyze possible consistent deformations of free tensor gauge field theories with specific symmetry properties, finding that only trivial or cosmological-constant-like deformations are allowed under certain conditions.

Contribution

It demonstrates that under locality and Poincare invariance, no non-trivial gauge algebra modifications are possible for these theories, with a unique simple deformation when limiting derivatives.

Findings

No non-trivial deformations of gauge algebra or transformations.

The only allowed deformation with limited derivatives is a cosmological-constant-like term.

Deformations are highly constrained by symmetry and locality assumptions.

Abstract

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p>1. Under the assumptions of locality and Poincare invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term.